Well posedness and asymptotic behavior of a wave equation with distributed time-delay and Neumann boundary conditions

Boumediène Chentouf; Aissa Guesmia

doi:10.1002/mma.5682

Well posedness and asymptotic behavior of a wave equation with distributed time-delay and Neumann boundary conditions

Boumediène Chentouf^*, Aissa Guesmia

^*Corresponding author for this work

Mathematics & Statistics

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

This paper is concerned with the asymptotic behavior analysis of solutions to a multidimensional wave equation. Assuming that there is no displacement term in the system and taking into consideration the presence of distributed or discrete time delay, we show that the solutions exponentially converge to their stationary state. The proof mainly consists in utilizing the resolvent method. The approach adopted in this work is also used to other physical systems.

Original language	English
Pages (from-to)	4584-4605
Number of pages	22
Journal	Mathematical Methods in the Applied Sciences
Volume	42
Issue number	13
DOIs	https://doi.org/10.1002/mma.5682
Publication status	Published - Sept 15 2019

Keywords

distributed time-time delay
exponential convergence
long time behavior
resolvent method
wave equation

ASJC Scopus subject areas

Mathematics(all)
Engineering(all)

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10.1002/mma.5682

Cite this

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abstract = "This paper is concerned with the asymptotic behavior analysis of solutions to a multidimensional wave equation. Assuming that there is no displacement term in the system and taking into consideration the presence of distributed or discrete time delay, we show that the solutions exponentially converge to their stationary state. The proof mainly consists in utilizing the resolvent method. The approach adopted in this work is also used to other physical systems.",

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AU - Guesmia, Aissa

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N2 - This paper is concerned with the asymptotic behavior analysis of solutions to a multidimensional wave equation. Assuming that there is no displacement term in the system and taking into consideration the presence of distributed or discrete time delay, we show that the solutions exponentially converge to their stationary state. The proof mainly consists in utilizing the resolvent method. The approach adopted in this work is also used to other physical systems.

AB - This paper is concerned with the asymptotic behavior analysis of solutions to a multidimensional wave equation. Assuming that there is no displacement term in the system and taking into consideration the presence of distributed or discrete time delay, we show that the solutions exponentially converge to their stationary state. The proof mainly consists in utilizing the resolvent method. The approach adopted in this work is also used to other physical systems.

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KW - exponential convergence

KW - long time behavior

KW - resolvent method

KW - wave equation

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Well posedness and asymptotic behavior of a wave equation with distributed time-delay and Neumann boundary conditions

Abstract

Keywords

ASJC Scopus subject areas

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